GCF of 747/348, 762/122
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 747/348, 762/122 i.e 3/21228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 747/348, 762/122.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 747/348,762/122?
Given fractions are 747/348,762/122
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 747/348,762/122, numerators are 747,762
Denominators are 348,122
The GCF of 747,762 is 3 .
LCM of 348,122 is 21228.
The greatest common factor of 747/348,762/122 = [GCF of 747,762]/[LCM of 348,122]= 3/21228
Therefore, the GCF of 747/348,762/122 is 3/21228.
To find the highest common factor of 747,762, we have to find the factors of both numbers and list the highest common factor.
The factors of 747 are 1, 3, 9, 83, 249, 747
The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762
The HCF of 747,762 is 3.
Lets's calculate GCF of 747,762
| 3 | 747, 762 |
| 249, 254 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 747,762 By Matching Biggest Common Factor Method
Now, list down the factors of 747
:1,3,9,83,249,747
Now, list down the factors of 762
:1,2,3,6,127,254,381,762
Greatest Common Factor
We found the factors 747,762 . The biggest common factor number is the GCF number.
So the greatest common factor 747,762 is 3.
Lets's calculate LCM of 348,122
| 2 | 348, 122 |
| 174, 61 |
∴ So the LCM of the given numbers is 2 x 174 x 61 = 21228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/21228
Therefore, the GCF of Fractions 747/348,762/122 is 3/21228
Least Common Multiple of 348,122 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 348,122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(348,122) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(348,122) x common factors =2 x 1 = 2
LCM(348,122) = ( 348 × 122 ) / 2
LCM(348,122) = 42456 / 2
LCM(348,122) = 21228
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FAQs on GCF of Fractions of 747/348, 762/122
1. What is the HCF of 747,762?
The HCF of 747,762 is 3
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 747/348, 762/122?
Answer: GCF of Numerators as per given numbers 747/348, 762/122 is
GCF of Numerators i.e. for 747,762 is 3
LCM of denominators i.e. for 348,122 is 21228.
Thus, GCF of Fractions is 3/21228.Finally, GCF of Fractions for 747/348, 762/122 is 3/21228.